Limit Theorems

This page will perform basic multiple regression analysis for the case where there are several independent predictor variables, X1, X2, etc., and one dependent or criterion variable, Y. Requires import of data from a spreadsheet.

Part of an online statistics textbook. Topics include: (1) Law of Large Numbers for Discrete Random Variables, (2) Chebyshev Inequality, (3) Law of Averages, (4) Law of Large Numbers for Continuous Random Variables, (5) Monte Carlo Method. There are several examples and exercises that accompany the material.

This resource briefly explains what a significance level is and how they are used in hypothesis testing. It also includes other links related to significance level such as "Type I error" and "significance test".

This applet simulates rolling dice to illustrate the central limit theorem. The user can choose between 1, 2, 6, or 9 dice to roll 1, 5, 20, or 100 times. The distribution is graphically displayed. This applet needs to be resized for optimal viewing.

For n = 50 to 400, in steps of size 5, this program computes and displays (1) the exact probability P(|A_n - p| >= epsilon), where A_n is the average outcome of n Bernoulli trials with probability p of success, and (2) the Chebyshev estimate p(1-p)/(n(epsilon^2)) for this probability. You can specify p and epsilon.

EasyCharts is a complete library of java chart components, chart applets, and chart servlets that enable programmers to add charts and graphs in java applications, web applications, and web pages with just a few lines of code. The java chart library includes bar charts, line charts, and pie charts and is highly configurable. The java chart library supports charts with multiple data series, overlay charts, drilldown charts, and interactive features such as zooming and scrolling of chart data.

The applets in this section of Statistical Java allow you to see how the Central Limit Theorem works. The main page gives the characteristics of five non-normal distributions (Bernoulli, Poisson, Exponential, U-shaped, and Uniform). Users then select one of the distributions and change the sample size to see how the distribution of the sample mean approaches normality. Users can also change the number of samples. To select between the different applets you can click on Statistical Theory, the Central Limit Theorem and then the Main Page. At the bottom of this page you can make your applet selection. This page was formerly located at http://www.stat.vt.edu/~sundar/java/applets/